On the optimal redundancy allocation for multi-state series-parallel systems under epistemic uncertainty

In this paper, we study the redundancy allocation problem (RAP) for multi-state series–parallel systems (MSSPSs). For each multi-state component, the exact values of its state probabilities are assumed to be unknown, due to epistemic uncertainty (EU), and only conservative lower and upper bounds of them are given. The objective of the RAP is to simultaneously maximize the supremum and infimum of the system's uncertain availability, under a cost constraint. The problem is two-stage and multi-objective. In this work, we: 1. provide a linear-time algorithm to obtain the component state distribution, under which the uncertain system availability will be at its supremum or infimum; 2. show that the problem is reducible to one-stage; 3. analyze the landscape of MSSPS RAP under EU and propose a modified NSGA-II, with targeted designs of repair and local search operation. The proposed algorithm is compared with standard NSGA-II on multiple benchmarks. The results show that the proposed algorithm significantly outperforms the standard NSGA-II in both optimality and time efficiency.